Stability of Volterra integrodifferential systems (Q1262495)

For the integrodifferential system \(dx/dt=Ax+\int^{t}_{0}C(t,s)x(s)ds\) sufficient stability conditions are formulated by means of a decomposition of the system and a subsequent application of a vector Lyapunov function. Only the case is considered when the subsystems \(dx_ i/dt=A_{ii}x_ i,\quad x_ i\in {\mathbb{R}}^{n_ i},\) obtained in the result of decomposition are asymptotically stable.